Freaky subdivision with n-gons (2.8)
A quick way to fix your topology:




Starting with the wrong number of vertices, having X > deleted faces only
Select the square's edges, and WSsubdivide with 7 cuts
Select both edge loops, and CtrlE > Bridge Edge Loops


EDIT:

.. but if you're subsurface modeling, as batFINGER points out, you really should be heading for a much lower number of vertices to make a circle in the end result:

4 sides .. Noticeably not octagonal under one level of subdiv., or circular under two. You can get away with it if you know it's never going to be close up. Shading artifacts, too. 

5.. Can't remember the last time I used it... 

6.. Quite a lot of things have 3-symmetry, and a hexagon makes a perfectly good circle

8.. By far the most common because of the shown topology - comes naturally out of a quad, the diagonals can be absorbed in 5-poles in a holding loop around the circle, or your beveled edges, so don't propagate around your model

.. any more than 8, probably large-scale structure rather than detail, or soaking up necessary loops from somewhere else in the model.

The Illustration is of 0,1,2 levels of subdivision on the various polygons, with a 32-circle in the middle for comparison.